Dependence of sum frequency field intensity on group velocity mismatches

The sum frequency field generated by mixing phase matched optical pulses in a nonlinear crystal is studied. Specifically, the field intensity at full width half maximum (FWHM) considered as a function of the group velocity mismatch between incident pulses, and also as a function of the mismatch between the generated pulse and one of the incident pulses, is analyzed by numerical and asymptotic techniques. Both mismatch types are allowed to be arbitrary. The FWHM intensity of the sum frequency field refers here to a cross-correlation measurement between pulses separated by a time delay to τ, where the FWHM is formed with respect to varying τ, rather than to the time-based FWHM of a sum-frequency-generated light pulse for a fixed τ. It is shown that the FWHM is fundamentally insensitive to mismatch between generated and incident fields, thus providing a justification for ignoring this term. On the other hand, the FWHM is shown to vary asymptotically linearly (coefficient ≈1) with the mismatch between incident pulses